Mathematics, 20.10.2019 12:30 Angel1107

The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?

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Answer from: lilspike420

123 3/11 dm102 8/11 dm

Step-by-step explanation:

The ratio of the linear dimensions (perimeter) is the square root of the ratio of area dimensions, so the larger : smaller ratio is ...

√(72/50) = √1.44 = 1.2

The sum of ratio units is 1.2 + 1 = 2.2, so each ratio unit stands for ...

(226 dm)/2.2 = 102 8/11 dm . . . . . the perimeter of the smaller triangle

Then the perimeter of the larger triangle is ...

1.2 × 102 8/11 dm = 123 3/11 dm . . . . the perimeter of the larger triangle

Answer from: Weser17

$\large\boxed{\dfrac{1130}{11}\ dm=102\dfrac{8}{11}\ dm\ and\ \dfrac{1356}{11}\ dm=123\dfrac{3}{11}\ dm}$

Step-by-step explanation:

We know: The ratio of the areas of similar triangles is equal to the square of the similarity scale.

Threfore:

$\text{If}\ \triangle_1\sim\triangle_2,\ \text{then}\ \dfrac{A_{\triangle_1}}{A_{\triangle_2}}=k^2$

We have

$A_{\triangle_1}=72\ dm^2\\\\A_{\triangle_2}=50\ dm^2$

Susbtitute:

$k^2=\dfrac{72}{50}\\\\k^2=\dfrac{72:2}{50:2}\\\\k^2=\dfrac{36}{25}\to k=\sqrt{\dfrac{36}{25}}\\\\k=\dfrac{\sqrt{36}}{\sqrt{25}}\\\\\boxed{k=\dfrac{6}{5}}$

We have the similarity scale.

We know: The ratio of the perimeters of similar triangles is equal to the similarity scale.

Therefore:

$\text{If}\ \triangle_1\sim\triangle_2,\ \text{then}\ \dfrac{P_1}{P_2}=k\to P_1=kP_2$

We have:

$P_1+P_2=226\ dm^2$

Substitute:

$k=\dfrac{6}{5},\ P_1=kP_2\to P_1=\dfrac{6}{5}P_2$

$\dfrac{6}{5}P_2+P_2=226\\\\\dfrac{6}{5}P_2+\dfrac{5}{5}P_2=226\\\\\dfrac{11}{5}P_2=226\qquad\text{multiply both sides by 5}\\\\11P_2=1130\qquad\text{divide both sides by 11}\\\\P_2=\dfrac{1130}{11}\\\\\boxed{P_2=102\dfrac{8}{11}\ dm}\\\\\\P_1=kP_2\to P_1=\dfrac{6}{5}\cdot\dfrac{1130}{11}\\\\P_1=\dfrac{6}{1}\cdot\dfrac{226}{11}\\\\P_1=\dfrac{1356}{11}\\\\\boxed{P_1=123\dfrac{3}{11}\ dm}$

Answer from: Quest

step-by-step explanation:

3024 rhe base is what up in worry about

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what i...

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