In a right angled triangle, length of hypotenuse is 13 cm. If length of perpendicular 3cm less than thrice of length of base, then find the perimeter of triangle.
Answers
Answer:
The hypotenuse of the right angled triangle(h) = 25 cm
Step-by-step explanation:
Let the one side of a right angled triangle(b) = x and
The other side of a right angled triangle (h) = (3x + 3)
Given, the area of the triangle = 84 cm^{2}cm
2
To find, the hypotenuse of the triangle (h) = ?
We know that,
The area of a right angled triangle = \dfrac{1}{2} bh
2
1
bh
⇒ \dfrac{1}{2} x(3x+3) = 84
2
1
x(3x+3)=84
⇒ x(3x+3) = 84 × 2 = 168
⇒ 3x^{2} +3x-168=03x
2
+3x−168=0
Dividing by 3, we get
⇒ x^{2} +x-56=0x
2
+x−56=0
⇒ x^{2} +8x-7x-56=0x
2
+8x−7x−56=0
⇒ x(x + 8) - 7(x + 8) = 0
⇒ (x + 8)(x - 7) = 0
⇒ x + 8 = 0 or, x - 7 = 0
⇒ x = - 8 or, x = 7 [ ∵ -7 is not possibe because side never be negative]
⇒ x = 7
∴ 3x + 3 = 3 × 7 + 3 = 24
In a right angled triangle ,
Hypoyaneous, h = \sqrt{b^{2}+ p^{2}}
b
2
+p
2
=\sqrt{7^{2}+ 24^{2}}=\sqrt{49+576} =\sqrt{625} =25 cm=
7
2
+24
2
=
49+576
=
625
=25cm
Thus, the hypotenuse of the right angled triangle(h) = 25 cm
Answer:
Let the hypotenuse be x. Then the other sides are (x−4) and (x−8) .
x2=(x−4)2+(x−8)2
⟹x2=x2−8x+16+x2−16x+64
⟹x2−24x+80=0
⟹(x−20)(x−4)=0
x=20orx=4
if x=4cm , then the other sides are negative, hence this cannot be the result.
x=20cm tells us that the other sides are 16cm and 12cm .
Perimeter=20+12+8=40cm
Area=12×16×12=96cm2