The area of a right angled triangle is 165 m2.

Question:

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

Solution:

Let the base of the right triangle be $=x$ metres and the altitude $=(x+7)$ metres Then

According to question,

Areas of the right triangle $=165 \mathrm{~m}^{2}$

And as we know that the area of the right triangle $=\frac{1}{2} \times$ base $\times$ height

$\frac{1}{2} \times x \times(x+7)=165$

$x^{2}+7 x=330$

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

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

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

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

$(x-15)=0$

$x=15$

or

$(x+22)=0$

$x=-22$

Since negative value is not possible. So =15 m

Therefore the altitude is

$=(x+7)$

$=15+7$

$=22$

Hence, base of the right triangle be $15 \mathrm{~m}$ and altitude be $22 \mathrm{~m}$