Question

The sides of a triangle are 25cm,39cm and 56cm. Find (I) area, (ii) the length of the perpendicular drawn from the opposite vertex to the side of 25 cm.

Answer 1

Answer :

$\boxed{\boxed{\mathsf{Area = 420cm^2 \: and \: Height = 33.6cm}}}$

Step-by-step Explanation :

Given

• The sides of a triangle are 25cm,39cm and 56cm.

To Find

• (i) Area of triangle .
• (ii) The length of the perpendicular drawn from the opposite vertex to the side of 25 cm.

Solution

(i) Area Of The Triangle

Now according to question let the

$\mathsf{\longrightarrow \: First \: Side \: (a) = 25cm}$

$\mathsf{\longrightarrow \: Second \: Side \: (b) = 39cm}$

$\mathsf{\longrightarrow \: Third \: Side \: (c) = 56cm}$

Now by Heron's Formula we have,

$\boxed{\mathsf{\bigstar \: Area\: of \: Triangle = \sqrt{s(s - a)(s - b)(s - c)}}}$

Where

$\mathsf{\longrightarrow \: (a) = First \: Side \: = 25cm}$

$\mathsf{\longrightarrow \: (b) = Second \: Side \: = 39cm}$

$\mathsf{\longrightarrow \: (c) = Third \: Side \: = 56cm}$

$\longrightarrow \: \implies \mathsf{S = Semi - Perimeter}$

$\longrightarrow \: \longrightarrow \mathsf{S = \dfrac{a + b + c}{2}}$

$\longrightarrow \: \longrightarrow \mathsf{S = \dfrac{25cm + 39cm + 56cm}{2}}$

$\longrightarrow \: \longrightarrow \mathsf{S = \dfrac{120cm}{2} = 60cm}$

Now putting above values in formula we have,

$\longrightarrow \:\mathsf{Area = \sqrt{s(s - a)(s - b)(s - c)}}$

$\longrightarrow \:\mathsf{Area = \sqrt{60(60 - 25)(60 - 39)(60 - 56)}}$

$\longrightarrow \:\mathsf{Area = \sqrt{60(35)(21)(4)}}$

$\longrightarrow \:\mathsf{Area = \sqrt{2 \times 2 \times 3 \times 5(5 \times 7)(3 \times 7)(2 \times 2)}}$

$\longrightarrow \:\mathsf{Area = \sqrt{ {2}^{2} \times {2}^{2} \times {3}^{2} \times {5}^{2} \times {7}^{2} }}$

$\longrightarrow \:\mathsf{Area = 2 \times 2 \times 3 \times 5 \times 7 }$

$\longrightarrow \:\mathsf{Area = 420cm^2}$

(ii) Height with base (a)

Now we also know that ,

$\boxed{\mathsf{\bigstar \: Area \: of \: Triangle = \dfrac{1}{2} \times Base \times Height}}$

Where,

$\mathsf{\longrightarrow \: Base = a = 25cm}$

$\mathsf{\longrightarrow \: Height = h = To \: Find}$

$\mathsf{\longrightarrow \: Area = 420cm}$

Now putting this value in above formula we have,

$\mathsf{ Area \: of \: Triangle = \dfrac{1}{2} \times Base \times Height}$

$\mathsf{ 420cm^2 = \dfrac{1}{2} \times 25cm \times Height}$

$\mathsf{ 420cm^2 \times 2 = 25cm \times Height}$

$\mathsf{ Height = \dfrac{840cm^2}{25cm}}$

$\mathsf{ Height = 33.6cm}$

$\rule{300}{1}$

Answer 2

Answer:

ANSWER IS 33.6 CM

Step-by-step explanation:

Hence, Height is 420×2/25

Hence it is help you