Question

The shortest side of a right triangle is 7 inches long. The difference between the lengths of the other two sides is 1 inch. Find the missing sides. Use exact values.

longer leg: Inches
hypotenus: Inches

Answer 1

right-angled triangle

a= shortest side = 7 inches

b= other side of right angle

c= hypotenuse

we know that :

a= 7inches

c-b=1

if c-b=1, then c= 1+b

apply Pythagoras' theorem

a²+b² = c²

7²+b²= (b+1)²

49+b² = b²+2b+1

b²-b²-2b=1-49

-2b=-48

b= 24

b = 24 inches

calculate c (hypotenuse)

c²=a²+b²

c²= 7²+24²

c= V625=25

c= 25 inches

longer leg: 24Inches

hypotenus:25 Inches

the difference between the lengths of the other two sides is 1 inch:

b=24

c= 25

the difference 25-24= 1 inch

Explanation: