Question

the area of triangle is 160 cm2. if its height is 16 cm, them find its base.​

Answer 1

$Area \: of \: Triangle = 160 \: {cm}^{2}$

$Base = 16 \: cm$

$Altitude = \frac{Area \times 2}{Base}$

$= \frac{160 \times 2}{16}$

$= \frac{320}{16}$

$= 20 \: cm$

Answer 2

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Given:-

Triangle

Area Triangle = 80 cm^2

Base(B) = x cm

Height(H) = x - 6 cm

Find:-

Base(B) and Height(H)

Use Triangle Area Formula

A = 1/2 B H or 80 = 1/2 x(x - 6) Multiply both sides of the equation by 2

160= x(x - 6) Remove parentheses

160= x^2 - 6x Subtract 160 from both sides of the equation getting everything on one side of the equation equal 0.

X^2 - 6x - 160 = 0 Factor

(x - 16)(x + 10) = 0 => x = 16 or x = -10 by the Zero Product Rule x ∈ {16, -10} ✅

-10 is rejected since B > 0 & H > 0 (Measurements are positive)

Therefore: x = 16 => Base = x = 16 cm. & Height = x - 6 = 10 cm. ✅

Double Check: 80 = 1/2(16)(10) = 1/2(160) = 80 ✅ ✅

Answer: Base = 16 cm. and Height = 10 cm.