Question

The base and height of a triangle are in the ratio 4: 5. If the area is 640 sq. cm, find the base and height.​

Answer 1

base = 32 cm , height = 40 cm

Explanation:

ratio of base : height = 4 : 5 = 4x : 5x ( x is a multiplier )

The area (A) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the height ) , then

A =
`(1)/(2)` × 4x × 5x = 2x × 5x = 10x²

given A = 640 , then

10x² = 640 ( divide both sides by 10 )

x² = 64 ( take square root of both sides )

x =
`√(64)` = 8

Then

base = 4x = 4 × 8 = 32 cm

height = 5x = 5 × 8 = 40 cm