#### Question

The area of a right angled triangle is 165 m^{2}. Determine its base and altitude if the latter exceeds the former by 7 m.

#### Solution

Let the base of the right triangle be x meters and the altitude (x + 7) meters Then

According to question,

Areas of the right triangle = 165 m^{2}

And as we know that the area of the right triangle = `1/2xx"base"xx"height"`

`1/2xx x xx(x+7) = 165`

x^{2} + 7x = 330

x^{2} + 7x - 330 = 0

x^{2} - 15x + 22x - 330 = 0

x(x - 15) + 22(x - 15) = 0

(x - 15)(x + 22) = 0

x - 15 = 0

x = 15

or

x + 22 = 0

x = -22

Since negative value is not possible. So *x *= 15 m

Therefore the altitude is

= x + 7 = 15 + 7 = 22

Hence, base of the right triangle be 15m and altitude be 22m.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Area of a Right Angled Triangle is 165 M2. Determine Its Base and Altitude If the Latter Exceeds the Former by 7 M. Concept: Solutions of Quadratic Equations by Factorization.