Question

the area of a right angles triangle is 165 m².
Determine the measure of base and altitude if the measure of altitude is 7m more than the measure if base .

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Answer 1

Answer:

Let the base be x

Hence, Altitude = x+7

According to question⬅️⬅️⬅️⬅️⬅️⬅️

$\frac{1}{2} \times x \times (x + 7) = 165 \\ \frac{1}{2} \times {x}^{2} + 7x = 165 \\ {x}^{2} + 7x = 330 \\ {x}^{2} + 7x - 330 = 0 \\ (x + 22)(x - 15) \\ \\ \: so \: x = 15{as \: base \: cant \: be \: negative}$

So Base = 15 m

Altitude = 22 m

Answer 2

$\Huge{\blue{\underline{\textsf{Answer}}}}$

The length of the base is 15m and altitude is 22m.

$\large{\red{\underline{\tt{Explanation}}}}$

Let the base be x

The altitude exceeds the base by 7m.......(given)

∴ Altitude = x+7

Area of right angle triangle = $\sf\dfrac{1}{2}$ × Base × Height

So, 165 = $\sf\dfrac{1}{2}$ × x × (x+7)

$\implies\rm 165×2=x^2+7x$

$\implies\rm 330=x^2+7x$

$\implies\rm x^2+7x-330=0$

$\implies\rm x^2+22x-15x-330=0$

$\implies\rm x(x+22)-15(x+22)=0$

$\implies\rm (x+22)(x-15)=0$

$\implies\rm x=-22,15$

∴ Base = 15m

Altitude = 15+7 = 22m

∴ The length of base is 15m and Altitude is 22m.