Question

The base and height of the triangle are in the ratio of 3:2 and its area is 108 cm square.find its base and height

Answer 1

Answer "and" explanation:

Given: Triangle

Ratio Base:Height = 2:3 Say 2X:3X

Area = 1/2 B x H = 300 cm^2

Find: Height and Base

Plan: Use the Area of a Triangle formula to get an equation to help to find the height and base.

Area Triangle = 1/2 Base x Height

A = 1/2 (2X)(3X) = 300 => 3X^2 = 300 Divide both sides of the equation by 3

X^2 = 100

X = √100 = 10

Therefore: Base = 2X = 20 cm, Height = 3X = 30 cm

Area = 1/2(20)(30) = 10(30) = 300 cm^2

Ratio = Base:Height = 20/30 = 2/3 = 2:3

Double Check: reasonable, rechecked ✅ ✅

Answer: Height = 30 cm, Base = 20 cm

Answer 2

The base and height of the triangle are 18 cm and 12 cm respectively.

Given:

the ratio of the base and height of the triangle = 3: 2

area of the triangle = 108 sq cm

To Find:

the base and height of the triangle

Solution:

let the base and height of the triangle be 3x and 2x

now, we know that area of a triangle = 1/2 × base × height

⇒ 108 = 1/2 × 3x × 2x

3x² = 108

x² = 36

x = √36

x = 6

⇒ 3x = 3 × 6 = 18

and 2x = 2 × 6 = 12

Thus, the base and height of the triangle are 18 cm and 12 cm respectively.

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