Mathematics, 30.10.2019 09:31 ichabella2010

The height of a triangle is 6 centimeters less than the base. the area of the triangle is 123.5 square centimeters. find the length of the base and the height of the triangle.

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Answer from: hannahbeccahxo9681

The length of base=19cm

The length of height=13cm

Given:

Area of the triangle A=123.5 $\mathrm{cm}^{2}$

Height of the triangle h=b-6

To find:

Length of the base

Length of the height

Step by Step Explanation:

Solution:

According to the formula, Area of the triangle

$\mathrm{A}=\frac{1}{2} b \times h$

Where b=Base of the triangle

h=Height of the triangle

We know the value of A=123.5 $\mathrm{cm}^{2}$ and also we know

h=b-6

Substitute these values in the above equation we get

123.5= $\frac{1}{2} b \times(b-6)$

247= $b^{2}-6 b$

$b^{2}-6 b-247=0$

The above equation is of the form

$A x^{2}+B x+C=0$

Compare the above two equations we get

A=1, B=-6, C=-247

$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(-247)}}{2(1)}$

$\frac{6 \pm \sqrt{36+4(247)}}{2}$

$\frac{6 \pm \sqrt{36+988}}{2}$

$\frac{6 \pm \sqrt{1024}}{2}$

$\frac{6 \pm 32}{2 a}$

$\frac{6+32}{2}OR\frac{6-32}{2}$

38/2 OR -26/2

The value of b can't be negative so we take

b=38/2=19cm

Though we know that

h=b-6=19-6=13cm

Result:

Thus the length values of b and h are 19 and 13 cm respectively

Answer from: Quest

step-by-step explanation:

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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