Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse?


The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse?


Grade:12

2 Answers

sushant singh
66 Points
10 years ago

hi,...this question also just need to picturise the triangle...

Let a and b be the two sides of the triangle such that a is longer than b. The statement "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle" may be formulated by

h = a + 2 or a = h - 2

The statement "the shorter side of the triangle is 7 centimeters less than the longer side" may be formulated

b = a - 7 or b = (h - 2) - 7 = h - 9

We now use Pythagoras’s theorem to write a third equation

h 2 = a 2 + b 2

Substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only:

h 2 = (h - 2) 2 + (h - 9) 2

Simplify and rewrite the above equation in standard form.

h 2 -22 h + 85 = 0

Solve for h.

h = 5 and h = 17.

Only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle. 

somil garg
30 Points
10 years ago

17

 

consider the longer side as x then hyp.=x+2

and shorter side =x-7

now apply hypotneous th.

sovle the quadratic eqn to get the ans 15&3 but 15 is longer  so reject 3

hence hyp =15+2=17

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free