Question

The sides of a triangle are p, q and r. If p + q =
45, q + r = 40 and p + r = 35, then find the area
of the triangle.
150 sq. units
ООО
200 sq. units
170 sq. units
120 sq. units​

Answer 1

Answer:

p+q=45,

q+r=40

p+r=35

p+q+r=

45+40+35=120sq.units

Answer 2

Solution

Given :-

• The sides of a triangle are p, q and r
• If p + q = 45, q + r = 40 and p + r = 35.

Find :-

• Area of triangle .

Explanation

We Have,

==> p + q =45_________(1)

==> q + r = 40_________(2)

and,

==> p + r = 35________(3)

Add equ(1) , equ(2) & equ(3)

==> 2(p + q + r) = 45 + 40 + 35

==> 2(p + q + r) = 120

==> p + q + r = 120/2

==> p + q + r = 60______________(4)

Keep value by equ(1)

==> 45 + r = 60

==> r = 60 - 45

==> r = 15

Again

keeo value by equ(2)

==> p + 40 = 60

==> p = 60 - 40

==> p =20

Now, keep value by equ(3)

==> 35 + q = 60

==> q = 60 - 35

==> q = 25

Now, Let

∆ ABC here,

Where,

• AB = 20
• BC = 25
• CA = 15

Now, We calculate Area of triangle

Using Formula

$\boxed{\tt{\:(Semi\:perimeter)\:=\:\dfrac{(AB+BC+CA)}{2}}}$

So,

==> Semi perimeter (S) = (20 + 25 + 15)/2

==> S = 60/2

==> S = 30

Now,

$\boxed{\tt{\:Area_{triangle}\:=\:\sqrt{S(S-AB)(S-BC)(S-CA)}}}$

keep value,

==> Area of triangle = √[30(30 - 20)(30-25)(30-15)]

==> Area of triangle =√(30×10×5×15)

==> Area of triangle = √( 10×10×5×5×3×3)

==> Area of triangle = 10 × 5 × 3

==> Area of triangle = 150 unit²

Hence

• Your answer will be option number (A).150 unit².

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