How many times is: FG longer than BC? EF longer than AB? JK

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your questions:

Determine the side lengths of the triangles.
From the grid:
For $\triangle$ ABC:
- Length of AB = 2 units
- Length of BC = 3 units
- Length of AC = $\sqrt{2^2 + 3^2} = \sqrt{4+9} = \sqrt{13}$ units
For $\triangle$ EFG:
- Length of EF = 4 units
- Length of FG = 6 units
- Length of EG = $\sqrt{4^2 + 6^2} = \sqrt{16+36} = \sqrt{52} = 2\sqrt{13}$ units
Answer 3.1.1.
The question asks: "How many times is FG longer than BC?"
$\frac{\text{FG}}{\text{BC}} = \frac{6}{3} = 2$
FG is 2 times longer than BC.
The answer is: $\boxed{\text{2 times}}$
Answer 3.1.2.
The question is structured as "JK ______ shorter than BC?". The word "shorter" is already provided. This implies we need to identify a side that is shorter than BC.
Length of BC = 3 units.
Looking at the sides of $\triangle$ ABC, AB has a length of 2 units.
Since $2 < 3$ , AB is shorter than BC.
The answer is: $\boxed{\text{AB}}$
Answer 3.1.3.
The question asks: "EF longer than AB?"
$\frac{\text{EF}}{\text{AB}} = \frac{4}{2} = 2$
EF is 2 times longer than AB.
The answer is: $\boxed{\text{2 times}}$
Answer 3.1.4.
The question is structured as "IJ ______ shorter than AB?". The word "shorter" is already provided. This implies we need to identify a side that is shorter than AB.
Length of AB = 2 units.
Looking at all sides in both triangles:
- AB = 2 units
- BC = 3 units
- AC = $\sqrt{13} \approx 3.6$ units
- EF = 4 units
- FG = 6 units
- EG = $2\sqrt{13} \approx 7.2$ units There is no side in either triangle that is shorter than AB. The answer is: $\boxed{\text{No side}}$
Answer 3.1.5.
The question asks: "Is $\triangle$ EFG an enlargement of $\triangle$ ABC? Explain your answer."
To determine if $\triangle$ EFG is an enlargement of $\triangle$ ABC, we compare the ratios of their corresponding sides:
$\frac{\text{EF}}{\text{AB}} = \frac{4}{2} = 2$ $\frac{\text{FG}}{\text{BC}} = \frac{6}{3} = 2$ $\frac{\text{EG}}{\text{AC}} = \frac{2\sqrt{13}}{\sqrt{13}} = 2$
Since the ratios of all corresponding sides are equal (the scale factor is 2), $\triangle$ EFG is an enlargement of $\triangle$ ABC.
The answer is:
$\boxed{\text{Yes, } \triangle\text{EFG is an enlargement of } \triangle\text{ABC. All corresponding sides are in the same ratio (scale factor of 2).}}$

How many times is: FG longer than BC? EF longer than AB? JK

Step-by-step solution

Determine the side lengths of the triangles.

Answer 3.1.1.

Answer 3.1.2.

Answer 3.1.3.

Answer 3.1.4.

Answer 3.1.5.

Still stuck on this one?

More Mathematics Questions