Question

A right isosceles triangle has an area of 98 cm ^2. FInd the length of each leg.

Answer 1

A drawing might help :)

Answer 2

if it was a square, the area would be 196

Answer 3

would you use the 45 45 90 to solve it?

Answer 4

i wouldn't

Answer 5

make a square then the area is the square of the side

Answer 6

i'm not sure i understand

Answer 7

There's no need for that. The area of a triangle is HALF the product of its base and height.

Now, I've drawn the triangle so that its base and height are the two legs of the isosceles triangle, which are congruent, so...

Here, both the base and height are x. What then is the area of the triangle (in terms of x)?

Answer 8

3x=98^2 ??

Answer 9

Where'd you get 3x?
Look the area of a triangle is typically given by
\[\Large A = \frac{bh}{2}\]
In your case however, both the base (b) and the height (h) are equal to x.

So your area is...?

Answer 10

i still very confused sorry

Answer 11

just replace both b and h with x.
What do you get? :)

Answer 12

98/2 =49

Answer 13

Stay with me here.
Replace both b and h with x, what do you get?

Answer 14

2x

Answer 15

No... x times x is not 2x, but rather...?

Answer 16

x^2

Answer 17

That's right.
So you have the area being equal to x^2 / 2
\[\Large \frac{x^2}{2}= 98\]

Now it's just a matter of solving for x. ^^

Answer 18

i got 14

Answer 19

how do you figure out the longest side?

Answer 20

You get that both legs measure 14.
The longest side is the hypotenuse.
Use the Pythagorean Theorem. :)

Answer 21

so 14^2+14^2 = c^2

Answer 22

c=19.799

Answer 23

I think i got it now! thank you so much for helping me i usually get things really quickly but this one stumped me thanks for sticking with me to help i really appreciate it!!!

Answer 24

No problem ^^
Good luck :)