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In $43-47,$ express each answer in simplest radical form.The length of each leg of an isosceles right triangle is $\sqrt{98}$ inches.a. Find the length of the hypotenuse.b. What is the perimeter of the triangle?

a) 14$i n$b) $(14+14 \sqrt{2}) i n$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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all right, so in this exercise, we are given that the length of one of the legs of a right I saw sleaze triangle is route 98 inches by means that the length of the other egg is also route 98 inches. The first portion of the question asks us to find the high pot news with second portion asks us to find the perimeter. So we're gonna start by finding the high pod news. Now, if you'll recall this Ah, iPod news value is given by the Pythagorean Fear. Um, a squared plus B squared equals C squared where a and fear the lengths of the lakes. So a squared would be the squared of 98 squared, which is just going to be 98. And that's going to also apply to the second leg. So we see that the high pot news squared length is 196. Now, if we want the actual high pot news link, we need to take the square root of both sides. Fortunately, 196 is a perfect square. It is the square of 14 so the length of the high pot news is 14 inches. Now, for the second part of the problem, we have to find the perimeter so that simply amounts to adding the quantities. 98 Route 98 plus Route 98 plus 14. Now let's see if we can simplify these radicals. A bit 98 is written. Can be decomposed into two times. 49 49 is a perfect square. We can factor it out as a seven, so we have a seven route to plus seven route, too, plus 14. Now we can combine the route to terms into 14 route, too, but you can't add a non radical terms with radical terms. However, we can factor 14 out of both of these terms and simply rewrite this as 14 times one plus route, too. So are high pot. News length is 14 and our perimeter length is 14 times the quantity one plus route, too

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