Question

May someone please help with the way please

Answer 1

Answer:

17.6 m²

Step-by-step explanation:

Given the ratio of similar shapes = a : b, then

area of shapes = a ² : b²

Δ PTQ and Δ PRS are similar and so the ratio of corresponding sides are equal, that is

PT : PR = 6 : 9 = 2 : 3, thus

ratio of areas = 2² : 3² = 4 : 9

let the area of Δ PQT be x, then using proportion

$\frac{4}{x}$ = $\frac{9}{x+22}$ ( cross- multiply )

9x = 4(x + 22) ← distribute

9x = 4x + 88 ( subtract 4x from both sides )

5x = 88 ( divide both sides by 5 )

x = 17.6

Thus area of Δ PQT = 17.6 m²