Question

The area of a triangle, whose base and the corresponding altitude are 15 cm and 4 cm, is equal to area of a right triangle whose one of the sides containing the right angle is 20 cm. Find the other side of this triangle. ​

Answer 1

Given :

• Area of a triangle whose base and height are 15 cm and 4 cm is equal to area of a right angled triangle whose one of the side containg right angle is 20 cm

To Find :

• The other side of right angled triangle

Solution :

Area of a triangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(triangle)} = \frac{1}{2} \times base \times height }}}}$

Let ,

• The Area of the right angled triangle be A₂
• The Area of the triangle be A₁

Let us calculate A₁. We are already given that base and height of the triangle as 15 cm and 4 cm. Substituting the values ,

$\\ : \implies \sf \: A_1 = \frac{1}{2} \times 15 \times 4$

$\\ : \implies{\underline{\boxed {\blue{\mathfrak{A_1 = 30 \: {cm}^{2} }}}}}$

Now , Let us calculate A₂. We are given that one of the containing right angle as 20 cm . Let this side be base.

Substituting the values ,

$\\ : \implies \sf \: A_2 = \frac{1}{2} \times 20 \times h$

$\\ : \implies{\underline{\boxed{\blue {\mathfrak{A_2 = 10h}}}}}$

According to the question ,

$\\ : \implies \sf \: A_1 = A_2$

$\\ : \implies \sf \:30 = 10h$

$\\ : \implies \sf \: h = \frac{30}{10}$

$\\ : \implies{\underline{\boxed{\pink {\mathfrak{h = 3 \: cm}}}}} \: \bigstar$

Hence ,

• The other side of the right angled triangle is 3 cm.

Answer 2

Answer:

Given :-

• Area of a triangle whose base and height are 15 cm and 4 cm is equal to area of a right angled triangle whose one of the side containg right angle is 20 cm

To Find :-

Other side

Solution :-

As we know that

$\bf \red{Area \: of \: triangle = \frac{1}{2} \times b \times h}$

$\tt \implies Area = \dfrac{1}{2} \times 15 \times 4$

$\tt \implies \: Area = 1 \times 15 \times 2$

$\tt \implies \: Area = 30 \: {cm}^{2}$

Now,

Let's find Area of second triangle

$\bf \red{Area \: of \: triangle \: = \frac{1}{2} \times b \times h}$

$\tt \implies \: Area = \dfrac{1}{2} \times 20 \times h$

$\tt \implies \: Area = 10 \times h \:$

$\tt \implies \: Area = 10h$

Now,

Let's find height

$\tt \implies30 = 10h$

$\tt \implies \: h = \frac{30}{10}$

Hence :-

Height is 3 cm