Question

Two numbers must be the ratio 7:4 . the difference of their square is 297. find the number​.​

Answer 1

Answer:

1st number = 21 or -21

2nd number = 12 or -12

Step-by-step explanation:

Given in image.

If you have any doubt please comment.

Answer 2

$\large \text{Question:}$

Two numbers must be the ratio 7:4 . The difference of their square is 297. Find the number.

$\large \text{Given:}$

• Two numbers must be in the ratio of 7:4
• Difference of their square is 207.

$\large \text{Let:}$

• first number = 7x
• second number = 4 x

$\large \text{Answer:}$

Equation formed according to question:

$: \implies \sf{} {(7x)}^{2} - ( {4x)}^{2} = 297$

$: \implies \sf{} 49{x}^{2} - 16{x}^{2} = 297$

$: \implies \sf{} 33{x}^{2} = 297$

$: \implies \sf{} {x}^{2} = \frac{297}{33}$

$: \implies \sf{} {x}^{2} = \frac{ { \cancel{297}}^{ \: \: 9} }{{ \cancel{33}}^{ \: \: 1}}$

$: \implies \sf{} {x}^{2} = 9$

$: \implies \sf{} x = \sqrt{9}$

$: \implies \sf{} x = \sqrt{3 \times 3}$

$: \implies \star \boxed{\sf{} x = 3} \star$

$\text{Let's verify whether value of x is correct or not}$

put value of x in this equation:

$\sf{} {(7x)}^{2} - ( {4x)}^{2} = 297$

$: \implies\sf{} {(7 \times 3)}^{2} - ( {4 \times 3)}^{2} = 297$

$: \implies\sf{} {(21)}^{2} - ( {12)}^{2} = 297$

$: \implies\sf{} 441 - 144 = 297$

$: \implies \star \boxed{\sf{} 297= 297} \star$

$\gray{\bf{†Hence Vertified†}}$

$\text{Now finally let's find number}$

As we have supposed 1 number as 7x and we got value of x as 3

.°. first number = 7×3

first number = 21

As we have supposed 2 number as 4x and we got value of x as 3

.°. second number = 4×3

second number = 12

And all we are done!