Question

rectangle has a length of (5+2x) inches and a width of 10 inches. A triangle base of 30 inches and a height of (4x-10) inches. The area in square inches the rectangle is equal to the area in square inches of the triangle. What is the value of x ?

Answer 1

x = 4

Explanation:

the area (A) of a rectangle is calculated as

A = length × width

given length = 5 + 2x and width = 10 , then

A = 10(5 + 2x) = 50 + 10x

the area (A) of a triangle is calculated as

A =
`(1)/(2)` × base × height

given base = 30 and height = 4x - 10 , then

A =
`(1)/(2)` × 30 × 4x - 10 = 15(4x - 10) = 60x - 150

given that the 2 areas are equal, then equate the 2 expressions for A

60x - 150 = 50 + 10x ( subtract 10x from both sides )

50x - 150 = 50 ( add 150 to both sides )

50x = 200 ( divide both sides by 50 )

x = 4