Question

A right-angled triangle of base xcm and height (x-7)cm has a hypo
tenuse of (x+1)cm long. Find the value of x​

Answer 1

Answer:

$\huge\fbox{☘Answer}$

x^2+(x-7)^2=(x+1)^2

x^2+x^2–14*x+49=x^2+2*x+1

x^2–16*x+48=0

x12=8+-sqrt(8^2–48)=8+-sqrt(16)=8+-4

x1=4

x2=12

Solution x1=4 is not good because x-7=-3. Corrected after remark.

Check:

x=x2=12

12^2+(12–7)^2=(12+1)^2

144+25=169

169=169

Sides are 12,5,13.

Answer 2

Answer:

x=12,4

Step-by-step explanation:

hypo^2=base^2+height^2

(x+1)^2=x^2+(x-7)^2

x^2+2x+1=x^2+x^2-14x+49

2x^2-14×+49-x^2-2x-1=0

x^2-16×+48=0

(x-12)(x-4)=0

x=12,4