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.

Question

asked Jul 12, 2023 211k views

1 Answer

Wade Matveyenko · Answer 1 · 2023-07-17T03:59:56+0000

Answer:

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