We are told that Larry has a television with a diagonal of $42$ inches. He is buying a stand for his television, which measures $30$ inches by $36$ inches. We will check if the television fit the stand. To do so, we will compare the diagonals of the television and the stand.

Notice that the diagonal of the stand is the hypotenuse of the right triangle. Therefore, we can use the Pythagorean Theorem to find the length of the diagonal.

a^{2} + b^{2} = c^{2}

Now, let's substitute

a = 36

inches and

b = 30

inches into the above formula and then isolate the hypotenuse

c .

a^{2} + b^{2} = c^{2}

SubstituteII

$a = 36$ , $b = 30$

36^{2} + 30^{2} = c^{2}

▼

Solve for

c

CalcPow

Calculate power

1296 + 900 = c^{2}

AddTerms

Add terms

2196 = c^{2}

SqrtEqn

$LHS = RHS$

2196 = c

RearrangeEqn

Rearrange equation

c = 2196

SplitIntoFactors

Split into factors

c = 4 \cdot 9 \cdot 61

SqrtProd

$a \cdot b = a \cdot b$

c = 4 \cdot 9 \cdot 61

CalcRoot

Calculate root

c = 2 \cdot 3 \cdot 61

Multiply

c = 661

UseCalc

Use a calculator

c = 46.861498 \dots

RoundDec

Round to $1$ decimal place(s)

c \approx 46.9

Since a negative side length does not make sense, we only need to consider positive solutions. Therefore, the length of the diagonal of the stand is about

46.9

inches.

46.9 in . > 42 in .

Since the diagonal of the stand is larger than the diagonal of the television, we can conclude that the television will fit the stand.

Exercise

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