A rectangular painting has a diagonal measure of 17 inches and an area of 120 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.

Length = 8 inches

Width = 15 inches

Step-by-step explanation:

A rectangular painting has a diagonal measure of 17 inches and an area of 120 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.

Let:

a = length of painting

b = width of painting

Area of painting = 120 = ab

Pythagorean Theorem says

a² + b² = Diagonal²

a² + b²= 17²

[120 =ab means b= 120/a]

a² + (120/a)² = 17²

Multiply through by a²

a⁴ + 14400 = 289

z² + 14400 = 289z [for now, substitute z for a²]

z² - 289z + 14400 = 0

z² - 64z - 225z + 14400 = 0

z(z - 64) -225(z - 64) = 0

(z - 64)(z - 225) = 0

z - 64 = 0

z = 64

z - 225 = 0

z = 225

Note that:

z for a²

Hence:

a² = 64

a = √64

a = 8 inches

The same applies for b

b² = 225

b = √225

b = 15 inches

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq