A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the lengt
h and width of the garden.
1 answer:
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Answer:
The Proof is below.
Step-by-step explanation:
Given:
To Prove:
Proof:
In ΔLPM and ΔNPM
……….{Given}
……….{Given}
……….{Reflexive Property}
ΔLPM ≅ ΔNPM ….{ By Side-Side-Side congruence test}
∴ ∠LMP ≅ ∠NMP ...{Corresponding parts of congruent triangles (c.p.c.t).}.....( 1 )
Now In ΔLMQ and ΔNMQ
……….{Given}
∠LMQ ≅ ∠NMQ ..........{From 1 above}
……….{Reflexive Property}
ΔLMQ ≅ ΔNMQ ....{ By Side-Angle-Side Congruence test}
∴ ...{Corresponding parts of congruent triangles (c.p.c.t).}.....Proved
Answer:
#5: 180 paperclips in total.
#6: 126 stamps in total.
#7: Elena should give Lucy 15 colored pencils.
Step-by-step explanation:
This explanation solves each question by setting a single unknown, .
Let the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.
Initially:
- Antonio:
paperclips;
- Abby:
Antonio gives paperclips to Abby. After that,
- Antonio:
paperclips;
- Abby:
paperclips.
Abby now possess twice as many paperclips as Antonio does. In other words,
.
By the distributive property:
.
Substract from both sides
.
Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.
<h3>#6</h3>Similarly, let be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.
Initially:
- Emily:
- Jasmine:
After Emily gives stamps to Jasmine:
- Emily:
stamps;
- Jasmine:
stamps.
Jasmine now possesses twice as many stamps as Emily does. In other words,
.
.
Jasmine used to possess 126 stamps. Now she possesses stamps after receiving
stamps from Emily.
Let the number of pencils that Elena needs to give to Lucy be .
Initially:
- Elena: 60 pencils;
- Lucy: 26 pencils.
After Elena gives pencils to Lucy:
- Elena:
pencils;
- Lucy:
pencils.
Elena should now possess four more pencils than Lucy does. In other words,
.
.
.